Factorisation by Splitting the Middle term

Transcript

Factorisation by Splitting the Middle term Suppose we want to factorise x2 + 7x + 12 We factorise it by splitting the middle term x2 + 7x + 12 = x2 + 4x + 3x + 12 = x(x + 4) + 3(x + 4) = (x + 3) (x + 4) Let’s do more examples Splitting the middle term method We need to find two numbers whose Sum = 7 Product = 1 × 12 = 12 Since sum and product both are positive, both numbers are positive The factorization of 〖4𝑥〗^2+8𝑥+3 is (a) (𝑥+1) (𝑥+3) (b) (2𝑥+1)(2𝑥+3) (c) (2𝑥+2) (2𝑥+5) (d) (2𝑥−1) (2𝑥−3) 4x2 + 8x + 3 = 4x2 + 2x + 6x + 3 = 2x(2x + 1) + 3(2x + 1) = (2x + 3) (2x + 1) ∴ Correct answer is (b) Splitting the middle term method We need to find two number whose Sum = 8 Product = 4 × 3 = 12 Since sum and product both are positive, both numbers are positive Factorise 5√5 𝑥^2+30𝑥+8√5 5√5 𝑥^2+30𝑥+8√5 = 5√5 x2 + 20x + 10x + 8√5 = 5x(√5x + 4) + 2√5(√5x + 4) = (5x + 2√𝟓) (√𝟓x + 4) Splitting the middle term method We need to find two number whose Sum = 30 Product = 5 √5 × 8 √5 = 40 × 5 = 200 Since sum and product both are positive, both numbers are positive